5 Answers
5

The Talmud (Chulin 91b) examines the angels' Divine service and concludes, "There exist three categories of angels who sing G-d's praise. The first group exclaims the blessing 'Holy' once. A second assembly praises G-d twice, 'Holy, holy.' And the third set repeats the acclaim three times, 'Holy, holy, holy is the L-rd of hosts'."

The Talmud there discusses other aspects of the Angels' songs, including frequency and that they have to wait for the Jews to sing praises before they can (which brings to mind this story told by the Ba'al Shem Tov).

There are different types of angels, as we were taught. And the question of what they do depends on what types of angels they are. Some interpretations of the Sepher Yetzirah tells us that some angels were actually "agents" of creation, each representing the different stages of creation ("stages" were , of course, just based on our perception), thus, it was written:

each angel has a specific job. once their job is completed, the angel is not needed any more and vanishes. there are some angels which "live on" forever: (you say every night) malach Gavriel, malach Uriel, malach Michael etc.

yes the 3 angles of Avrham once their duty was fulfilled they were not needed anymore.
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my rebbi's talmidApr 26 '10 at 3:40

Some angels do vanish, but not the three that visited Avraham , they were Rephael, Michael and Gabriel. I think Rambam says that every moment there are angels that come into existence and are then quickly destroyed once their task is complete.
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zaqAug 8 '11 at 17:30

Rash"i on B'reshis 16:13 alludes to the fact when he mentions that the conversation Hagar had with what appeared to be one angel was actually with a succession of 4 different angels.
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WAFMay 13 '12 at 14:33

via The Guide of the Perplexed Part II chapter VI: Bereshis Rabbah, chapter 1, "One angel does not perform two things, and two angels do not perform one thing" & Bereshis Rabbah, chapter 78 "Every day God creates a legion of angels; they sing before Him, and disappear."
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zaqMay 14 '12 at 21:13

The concept of the Angels and Heaven is extremely esoteric, and the prophecies which relate first hand visions of Heaven are not to be taken literally, namely Ezekiel and Isaiah. Rambam defines many of the words used in the accounts, and how they should be properly translated in order to understand it. He teaches that the angels are strongly interwoven with "God's Glory", the creation, chaos and the natural-laws of the universe, what he calls "divine science". It's not really supposed to be discussed as it can be very easily misunderstood, however, in The Guide of the Perplexed, the Rambam does his best to explain it without violating the prohibition.

God is incorporeal and unchanging, as such He uses messengers to interact with lower worlds that require physical-interaction.

Angels don't have free will the way man does and they have to follow Hashem's will. There is a bit of leeway in how they can fill God's command, but ultimately there is a governing-command that they must follow. In nature, it is similar to how a leaf floats down from a tree, it will definitely fall to the ground but how it gets there is unpredictable.

I wasn't clear. Angels DO have some free will, just not the same way man has. He discusses it in Part II chapter 6 & 7. I thought I read the leaf metaphor in the Moreh Han'vuchim as well, but I'm not having any luck finding it right now.
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zaqMay 14 '12 at 21:18

No problem. There are definitely other places in the book where he touches on the type of free will angels have, like the beginning of part three where he talks about the ophanim, chayos, cherubim, and serafim. If I find others that apply I'll post more.
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zaqMay 15 '12 at 2:07